Asymptotic behavior of bootstrapped extreme order statistics under unknown power normalizing constants

Abstract Bootstrapping is a powerful statistical technique, but its reliability for analyzing extreme events with unknown power normalization remains unclear. This paper addresses this issue by exploring the asymptotic properties of bootstrapped extreme order statistics under unknown power normalizing constants. Different estimators of the power normalizing constants are considered. The consistency properties of bootstrapped extreme order statistics with the estimated power normalizing constants are investigated. An extensive simulation study is conducted to identify an optimal bootstrap sample size under power and linear normalization. This study is based on how closely the bootstrapped extreme order statistics align with their theoretical asymptotic limits.